Question

The units digit of $1!+2!+3!+...+49!$ is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

We have to evaluate unit's digit of the sum $1!+2!+3!+...+49!$
We have,
$1!=1$
$2!=2$
$3!=6$
$4!=24$
$5!=120$
$6!=6(5!)=720$
$7!=7\times 6(5!)=$ a multiple of $10$.
Clearly, factorial of every number after $4$ will be a multiple of $10$. So, factorial value of every number after $4$ will have $0$ at its unit's place.
Unit digit of required sum $1+2+6+4+0+...$ is $3$.